Project #14822 - Statistics - Confidence Intervals for Proportions

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I am paying $10 dollars for this homework assignment to be completed by Monday 5 PM only 9 questions.

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1.

Which of the following statements are true?

i. The sample proportion is equal to the population proportion

ii. We expect the sample proportion to be in the neighborhood of the population proportion since the sampling distribution for a proportion is normal and 95% of the sample proportions should be within +/- 2 standard deviations of the population proportion.

iii. We expect 95% confidence intervals to contain the population proportion 95% of the time.

iv. A 95% confidence interval always contains the population proportion

Which of the following criteria must be met to find a confidence interval for the population proportion?

A. The data values in the sample must be independent. B. The data must come from a random sample. C. The sample size must be less than 10% of the population size. D. You must expect at least 10 "successes" and at least 10 "failures", that is np ≥ 10 and nq ≥ 10

The St. Petersburg Times recently sponsored a poll asking the question, "Do you favor vouchers for students in private schools?" The article describing the poll says that it "is based on telephone interviews with 356 adults in Pinellas County." The article reported that 37% favored vouchers for private schools and gives the margin of error as 4 percentage points for 95% confidence. Find the 95% confidence interval for the true percent of adults in Pinellas County who favor vouchers for private schools.

In January 2002, two students made worldwide headlines by spinning a Belgian Euro 250 times and getting 140 heads--that is 56% heads. That makes the 90% confidence interval have a lower bound of 51% and an upper bound of 61%. Interpret this result.

A) Between 51% and 61% of all Euros are unfair. B) We are sure that in this experiment this Euro landed on heads on between 51% and 61% of the spins. C) We are 90% confident that the population proportion of heads for the spun Euro is between 51% and 61%. D) If you spin a Euro many times, you can be 90% sure of getting between 51% and 61% heads. E) 90% of all euros that are spun will land heads between 51% and 61% of the time.

This section is an appendix containing density tools to be used to solve various problems. The seventh density tool is for finding confidence intervals for proportions. Use that tool to solve the following problem.

Pye and Associates recently conducted a survey to determine the percent of adult county residents who believe that students in public high schools should wear uniforms to school. The telephone poll of 325 adults found that 35% of the adults believe that public high school students should wear uniforms to school. Determine the 95% confidence interval for the true proportion of adults in the county who believe public high school students should wear uniforms.

Show the lower bound. Show your answers as percents rounded to TENTHS of a percent.

This section is an appendix containing density tools to be used to solve various problems. The seventh density tool is for finding confidence intervals for proportions. Use that tool to solve the following problem.

Pye and Associates recently conducted a survey to determine the percent of adult county residents who believe that students in public high schools should wear uniforms to school. The telephone poll of 325 adults found that 35% of the adults believe that public high school students should wear uniforms to school. Determine the 95% confidence interval for the true proportion of adults in the county who believe public high school students should wear uniforms.

Show the upper bound. Show your answers as percents rounded to TENTHS of a percent.

This section is an appendix containing density tools to be used to solve various problems. The seventh density tool is for finding confidence intervals for proportions. Use that tool to solve the following problem.

Direct mail advertisers send solicitations (that is "junk mail") to thousands of potential customers in the hope that some will buy the company's products. The response rate is usually quite low. Suppose a company wants to test the response rate for a new flyer format. The company randomly selects 1000 from its mailing list of over 200,000 people. Their sample results in orders from 112 people.

Create a 90% confidence interval for the percentage of people the company contacts who may buy something.

Show the lower bound. Show your answers as percents rounded to TENTHS of a percent.

This section is an appendix containing density tools to be used to solve various problems. The seventh density tool is for finding confidence intervals for proportions. Use that tool to solve the following problem.

Direct mail advertisers send solicitations (that is "junk mail") to thousands of potential customers in the hope that some will buy the company's products. The response rate is usually quite low. Suppose a company wants to test the response rate for a new flyer format. The company randomly selects 1000 from its mailing list of over 200,000 people. Their sample results in orders from 112 people.

Create a 90% confidence interval for the percentage of people the company contacts who may buy something.

Show the upper bound. Show your answers as percents rounded to TENTHS of a percent.

This section is an appendix containing density tools to be used to solve various problems. The seventh density tool is for finding confidence intervals for proportions. Use that tool to solve the following problem.

Direct mail advertisers send solicitations (that is "junk mail") to thousands of potential customers in the hope that some will buy the company's products. The response rate is usually quite low. Suppose a company wants to test the response rate for a new flyer format. The company randomly selects 1000 from its mailing list of over 200,000 people. Their sample results in orders from 112 people.

The company will use the new flyer format if it produces at least a 10% return. Based on the 90% confidence interval that you found in the previous problem, should the company adopt the new flyer format?

A) Yes, based on the confidence interval most of the time the population proportion of people who will buy is above 10%. B) No, based on the confidence interval for the population proportion of people who will buy, there is the chance that the population proportion is below 10%.